Problem: A piece of string fits exactly once around the perimeter of a square whose area is 144.  Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?
Answer: Since the area of the square is 144, each side has length $\sqrt{144}=12$.  The length of the string equals the perimeter of the square which is $4 \times 12=48$.  The largest circle that can be formed from this string has a circumference of 48 or $2\pi r=48$.  Solving for the radius $r$, we get $r=\frac{48}{2\pi} = \frac{24}{\pi}$. Therefore, the maximum area of a circle that can be formed using the string is $\pi \cdot \left( \frac{24}{\pi} \right)^2 = \frac{576}{\pi} \approx \boxed{183}$.